Vismodegib Combined With Atezolizumab in Platinum Resistant Ovarian, Fallopian Tube, and Primary Peritoneal Cancer

Inclusion Criteria: * Signed Informed Consent Form * Ability to comply with the study protocol, in the investigator's judgment * Histologically or cytologically confirmed epithelial ovarian, fallopian tube or primary peritoneal cancer * Platinum status, defined by disease progression during or following treatment with platinum-based chemotherapy within 6 months of completing therapy * Measurable or non-measurable but evaluable disease per RECIST v1.1 {Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation.} * Availability of a representative tumor specimen for exploratory biomarker research will be required for 12 patients (see Section 5.4.5 for information on tumor specimens) * ECOG Performance Status of 0-1 * Life expectancy ≥ 3 months * Adequate hematologic and end-organ function, defined by the following laboratory test results, obtained within 14 days prior to initiation of study treatment: ANC ≥ 1.5 ⋅ 109/L (1500/μL) without granulocyte colony-stimulating factor support; Lymphocyte count ≥ 0.5 ⋅ 109/L (500/μL); Platelet count ≥ 100 ⋅ 109/L (100,000/μL) without transfusion; Hemoglobin ≥ 80 g/L (8 g/dL) (Patients may be transfused to meet this criterion.) * AST, ALT, and alkaline phosphatase (ALP) ≤ 2.5 ⋅ upper limit of normal (ULN), with the following exceptions: * Patients with documented liver metastases: AST and ALT ≤ 5 ⋅ ULN * Patients with documented liver or bone metastases: ALP ≤ 5 ⋅ ULN * Serum bilirubin ≤ 1.5 ⋅ ULN with the following exception: * Patients with known Gilbert disease: serum bilirubin ≤ 3 ⋅ ULN * Serum creatinine ≤ 1.5 ⋅ ULN * Serum albumin ≥ 25 g/L (2.5 g/dL) * For patients not receiving therapeutic anticoagulation: INR or aPTT ≤ 1.5 ⋅ ULN * For patients receiving therapeutic anticoagulation: stable anticoagulant regimen * Negative HIV test at screening, with the following exception: patients with a positive HIV test at screening are eligible if they are stable on anti-retroviral therapy, have a CD4 count \> 200, and have an undetectable viral load. * Negative hepatitis B surface antigen (HBsAg) test at screening * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods as defined below: * Women must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 5 months after the final dose of atezolizumab and for 24 months after the final dose of vismodegib. Women must refrain from donating eggs during this same period. * A woman is considered to be of childbearing potential if she is postmenarchal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). The definition of childbearing potential may be adapted for alignment with local guidelines or requirements. * Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception. Exclusion Criteria: * Inability or unwillingness to swallow capsules * Inability or unwillingness to comply with study procedures * History of leptomeningeal disease * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently) o Patients with indwelling catheters (e.g., PleurX→) are allowed. * Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium \> ULN) * Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, or multiple sclerosis (see Appendix 9) for a more comprehensive list of autoimmune diseases and immune deficiencies), with the following exceptions: * Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study. * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. * Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: * Rash must cover \< 10% of body surface area * Disease is well controlled at baseline and requires only low-potency topical corticosteroids * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan (History of radiation pneumonitis in the radiation field (fibrosis) is permitted). * Active tuberculosis * Significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident) within 3 months prior to initiation of study treatment, unstable arrhythmia, or unstable angina * Major surgical procedure, other than for diagnosis, within 4 weeks prior to initiation of study treatment, or anticipation of need for a major surgical procedure during the study * History of malignancy other than ovarian cancer within 5 years prior to screening, with the exception of malignancies with a negligible risk of metastasis or death (e.g., 5-year OS rate \> 90%), such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, localized prostate cancer, ductal carcinoma in situ, or Stage I uterine cancer * Severe infection within 4 weeks prior to initiation of study treatment, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * Treatment with therapeutic oral or IV antibiotics within 2 weeks prior to initiation of study treatment * Patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study. * Prior allogeneic stem cell or solid organ transplantation * Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of an investigational drug, may affect the interpretation of the results, or may render the patient at high risk from treatment complications * Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during atezolizumab treatment or within 5 months after the final dose of atezolizumab * Current treatment with anti-viral therapy for HBV * Treatment with investigational therapy within 28 days prior to initiation of study treatment * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 \[IL-2\]) within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment * Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF-α agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions: * Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study after Principal Investigator confirmation has been obtained. * Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study. * History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins * Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation * Known allergy or hypersensitivity to any component of the vismodegib formulation * Agreement not to donate blood or blood products during the study and for 24 months after discontinuation of vismodegib. * Pregnancy or breastfeeding, or intention of becoming pregnant during study treatment or within 5 months after the final dose of atezolizumab and for 24 months after the final dose of vismodegib. * Women of childbearing potential must have a negative serum pregnancy test result within 14 days prior to initiation of study treatment.